Ultralight scalars can form superradiant clouds around rotating black holes. These may alter the dynamics of compact binaries and the ensuing waveform through orbital resonances and cloud ionization. We reexamine resonances involving states with nonzero decay width, deriving an effective treatment for resonances that are wider than the binary’s frequency chirp. We demonstrate the utility of this approach by calculating an upper bound for the cloud’s mass surviving up to the latest stages of the inspiral. Next, we study the accumulation of resonances with high-energy bound states. When these infinitely many, increasingly weak resonances are properly taken into account, they smooth out the “sharp features” in the binary’s evolution that had been attributed to the ionization of the cloud. We compare our Newtonian results with recent relativistic calculations, highlighting common features as well as discrepancies. Our conclusions emphasize the need to carefully incorporate resonances in boson cloud waveform modeling.

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• Classical black holes
• Dark matter
• Gravitational waves
• Axion-like particles